Explicit analytical formulation and exact inversion of decomposable fuzzy systems with singleton consequents

Fuzzy Feedback Linearizing Controller and Its Equivalence With the Fuzzy Nonlinear Internal Model Control Structure

“…In this paper, the inverse control methodology proposed in (Boukezzoula et al, 2003;Galichet et al, 2004) for handling nonaffine-in-control nonlinear systems is used. In this framework, the proposed controller design is based on the on-line analytic inversion of the fuzzy plant model.…”

“…The proposed inversion methodology is exact, noniterative and makes the determination of multiple solutions possible, thus allowing the handling of more general systems than the ones usually considered in the fuzzy control literature. A detailed discussion concerning our inversion method with regard to other fuzzy inversion techniques (Babuska, 1998;Baranyi et al, 1998) is given in (Boukezzoula et al, 2003;Galichet et al, 2004). Consequently, the developed inversion mechanism can be easily used for implementing inverse control strategies, as shown in the paper for dealing with feedback linearizing control and internal model control.…”

“…As an alternative, when the plant dynamics are represented by a fuzzy system, an exact and noniterative inverse model controller can then be designed based on the local inversion of the fuzzy model. Indeed, TS fuzzy systems with singleton consequences (Sugeno, 1999) can be easily and exactly inverted provided that the inputs are described using strict triangular partitions (Boukezzoula et al, 2003;Galichet et al, 2004).…”

“…According to the multi-linearity property of fuzzy subsystems as established in (Rovatti, 1998;Ying and Chen, 1997;Zeng and Singh, 1996a), it can be shown (Boukezzoula et al, 2003;Galichet et al, 2004) that the output of a fired fuzzy subsystem can be rewritten as follows:…”

“…When a TS fuzzy model (7) is used, an exact and noniterative inverse model can be designed based on the local inversion of the fuzzy model (Boukezzoula et al, 2003;Galichet et al, 2004). Indeed, when considering u(k) as the inversion control variable, the problem consists in finding all u(k)-solutions, the variables y(k), .…”